Flexure Plate FEA Validation

[waltx]

TL;DR

Unsure what formulas to use: hand calcs not matching up with FEA

Hello, I am unsure what steps to take when trying to validate a flexure plate. My hand calculations do not match up with my FEA and I am unsure what formulas I am supposed to be using for this situation. I've tried simplifying into a simple cantilevered beam but the results do not match up. Any help will be appreciated. Thank you!

 

[jrmichler]

You do not tell us what your analysis is trying to find out. Are you looking for deflection, deflected shape, strain, stress, or what? What are the assumptions in your hand calculations? How and where do your hand calculations differ from the FEA? Please discuss in full detail.

Your diagram implies that the part is modelled as a single piece with sharp corners. Is that a correct model of the real part? Please discuss in detail.

 

[waltx]

My analysis is trying to find the deformation of the plate. The assumptions that I've made before were to simplify it into a beam however that did not yield correct values. I am using the same young's modulus and force and simplifying it into a simple cantilever beam with the force at the end. I am using the formula deflection = (P*L^3)/(3*E*I). I am first trying to find the deflection for just the end portion to see if my simplifications are correct.

What am I doing wrong?

These are my boundary conditions.

Thanks for the help

 

[jrmichler]

Hand calculating this problem takes several steps. Here is how I would do it.

1) The thin parts are doing all of the deflecting, so start by eliminating the solid blocks. The two thin beams are combined into one.

2) The bottom of the resulting beam is fixed. The top is subject to a force plus a moment.

3) An applied force will deflect the beam. It rotates the end by an angle $\theta$.
4) Apply a moment to the end of the beam. Calculate the moment to rotate the end by $\theta$ in the opposite direction. The end of the beam is now vertical. It has displaced without rotation.
5) Calculate the angle $\beta$ at the midpoint of the beam.
6) Use the angle $\beta$ plus the width of the middle block to calculate the added horizontal displacement due to the width of the middle block.
7) The total displacement is the sum of the displacement of the beam plus the added displacement due to the width of the block.

 

[waltx]

Thank you so much for your help! It matches up with my FEA if my equations look wrong let me know. Other than that thank you so much for your help!